Quand le changement ne suffit pas: Réduction, absorbabilité et identification de la plasticité

Philibert Andriamanantena ()
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Philibert Andriamanantena: École Doctorale Modélisation Informatique - Université de Fianarantsoa , Laboratoire de Mathématique et Application de l’Université de Fianarantsoa

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Abstract: How can we distinguish a structural transformation from a mere variation in representation? Drawing on the critical program of Book I of the *Treatise on Adaptive Systems*, this article develops a constructive procedure that allows us to subject a claimed plasticity to three complementary tests: reduction, absorbability, and identification under an explicitly specified observational framework. The approach is illustrated using a decision-making system for granting microcredit, in which a time-varying decision rule, a variable contributive domain, and a parameter θ interpolating between two aggregation regimes are considered in succession. For a variable distribution, the introduction of an augmented state space shows—under an explicit hypothesis regarding the closure and representability of its evolution—how variability can be absorbed into the state of a system with a fixed distribution. For a variable contributive domain, a compatible extension to a universal domain allows us to test, in a similar manner, whether the observed variation constitutes a structural difference. Finally, for the family Hθ(f, µ) = θC(f, µ) + (1 − θ)S(f, µ), a conditional parametric injectivity proposition establishes that, for a fixed capacity, θ is distinguishable within the family of operators if and only if the two aggregation regimes C and S do not coincide over the entire admissible class. These results lead to a rigorous distinction between existence, representability, operability, contribution, observability, and identifiability. Above all, they show that an observable variation—even one that is parametrically identifiable—is not sufficient to establish irreducible plasticity: the difference must still resist competing transformations that could absorb it and remain distinguishable relative to the chosen observation framework. The article thus arrives at a precise set of specifications for any future construction: before proposing an adaptation operator, one must determine which variations cannot be reduced, absorbed, or rendered equivalent by a competing representation.

Keywords: absorbabilité et systèmes adaptatifs plasticité réduction absorbabilité espace d'état augmenté opérabilité contribution tribunal d'observation identifiabilité agrégation non additive; agrégation non additive; identifiabilité; tribunal d'observation; contribution; opérabilité; espace d'état augmenté; absorbabilité; réduction; plasticité; absorbabilité et systèmes adaptatifs; Réduction (search for similar items in EconPapers)
Date: 2026-10-15
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